[SPARK-15076][SQL] Add ReorderAssociativeOperator optimizer

## What changes were proposed in this pull request?

This issue add a new optimizer `ReorderAssociativeOperator` by taking advantage of integral associative property. Currently, Spark works like the following.

1) Can optimize `1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + a` into `45 + a`.
2) Cannot optimize `a + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9`.

This PR can handle Case 2 for **Add/Multiply** expression whose data types are `ByteType`, `ShortType`, `IntegerType`, and `LongType`. The followings are the plan comparison between `before` and `after` this issue.

**Before**
```scala
scala> sql("select a+1+2+3+4+5+6+7+8+9 from (select explode(array(1)) a)").explain
== Physical Plan ==
WholeStageCodegen
:  +- Project [(((((((((a#7 + 1) + 2) + 3) + 4) + 5) + 6) + 7) + 8) + 9) AS (((((((((a + 1) + 2) + 3) + 4) + 5) + 6) + 7) + 8) + 9)alteryx#8]
:     +- INPUT
+- Generate explode([1]), false, false, [a#7]
   +- Scan OneRowRelation[]
scala> sql("select a*1*2*3*4*5*6*7*8*9 from (select explode(array(1)) a)").explain
== Physical Plan ==
*Project [(((((((((a#18 * 1) * 2) * 3) * 4) * 5) * 6) * 7) * 8) * 9) AS (((((((((a * 1) * 2) * 3) * 4) * 5) * 6) * 7) * 8) * 9)alteryx#19]
+- Generate explode([1]), false, false, [a#18]
   +- Scan OneRowRelation[]
```

**After**
```scala
scala> sql("select a+1+2+3+4+5+6+7+8+9 from (select explode(array(1)) a)").explain
== Physical Plan ==
WholeStageCodegen
:  +- Project [(a#7 + 45) AS (((((((((a + 1) + 2) + 3) + 4) + 5) + 6) + 7) + 8) + 9)alteryx#8]
:     +- INPUT
+- Generate explode([1]), false, false, [a#7]
   +- Scan OneRowRelation[]
scala> sql("select a*1*2*3*4*5*6*7*8*9 from (select explode(array(1)) a)").explain
== Physical Plan ==
*Project [(a#18 * 362880) AS (((((((((a * 1) * 2) * 3) * 4) * 5) * 6) * 7) * 8) * 9)alteryx#19]
+- Generate explode([1]), false, false, [a#18]
   +- Scan OneRowRelation[]
```

This PR is greatly generalized by cloud-fan 's key ideas; he should be credited for the work he did.

## How was this patch tested?

Pass the Jenkins tests including new testsuite.

Author: Dongjoon Hyun <[email protected]>

Closes apache#12850 from dongjoon-hyun/SPARK-15076.

sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/optimizer/Optimizer.scala

@@ -94,6 +94,7 @@ abstract class Optimizer(sessionCatalog: SessionCatalog, conf: CatalystConf)
       FoldablePropagation,
       OptimizeIn(conf),
       ConstantFolding,
+      ReorderAssociativeOperator,
       LikeSimplification,
       BooleanSimplification,
       SimplifyConditionals,
@@ -737,6 +738,44 @@ object InferFiltersFromConstraints extends Rule[LogicalPlan] with PredicateHelpe
   }
 }
 
+/**
+ * Reorder associative integral-type operators and fold all constants into one.
+ */
+object ReorderAssociativeOperator extends Rule[LogicalPlan] {
+  private def flattenAdd(e: Expression): Seq[Expression] = e match {
+    case Add(l, r) => flattenAdd(l) ++ flattenAdd(r)
+    case other => other :: Nil
+  }
+
+  private def flattenMultiply(e: Expression): Seq[Expression] = e match {
+    case Multiply(l, r) => flattenMultiply(l) ++ flattenMultiply(r)
+    case other => other :: Nil
+  }
+
+  def apply(plan: LogicalPlan): LogicalPlan = plan transform {
+    case q: LogicalPlan => q transformExpressionsDown {
+      case a: Add if a.deterministic && a.dataType.isInstanceOf[IntegralType] =>
+        val (foldables, others) = flattenAdd(a).partition(_.foldable)
+        if (foldables.size > 1) {
+          val foldableExpr = foldables.reduce((x, y) => Add(x, y))
+          val c = Literal.create(foldableExpr.eval(EmptyRow), a.dataType)
+          if (others.isEmpty) c else Add(others.reduce((x, y) => Add(x, y)), c)
+        } else {
+          a
+        }
+      case m: Multiply if m.deterministic && m.dataType.isInstanceOf[IntegralType] =>
+        val (foldables, others) = flattenMultiply(m).partition(_.foldable)
+        if (foldables.size > 1) {
+          val foldableExpr = foldables.reduce((x, y) => Multiply(x, y))
+          val c = Literal.create(foldableExpr.eval(EmptyRow), m.dataType)
+          if (others.isEmpty) c else Multiply(others.reduce((x, y) => Multiply(x, y)), c)
+        } else {
+          m
+        }
+    }
+  }
+}
+
 /**
  * Replaces [[Expression Expressions]] that can be statically evaluated with
  * equivalent [[Literal]] values.

sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/optimizer/ReorderAssociativeOperatorSuite.scala

@@ -0,0 +1,63 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.spark.sql.catalyst.optimizer
+
+import org.apache.spark.sql.catalyst.dsl.expressions._
+import org.apache.spark.sql.catalyst.dsl.plans._
+import org.apache.spark.sql.catalyst.expressions._
+import org.apache.spark.sql.catalyst.plans.PlanTest
+import org.apache.spark.sql.catalyst.plans.logical.{LocalRelation, LogicalPlan}
+import org.apache.spark.sql.catalyst.rules.RuleExecutor
+
+class ReorderAssociativeOperatorSuite extends PlanTest {
+
+  object Optimize extends RuleExecutor[LogicalPlan] {
+    val batches =
+      Batch("ReorderAssociativeOperator", Once,
+        ReorderAssociativeOperator) :: Nil
+  }
+
+  val testRelation = LocalRelation('a.int, 'b.int, 'c.int)
+
+  test("Reorder associative operators") {
+    val originalQuery =
+      testRelation
+        .select(
+          (Literal(3) + ((Literal(1) + 'a) + 2)) + 4,
+          'b * 1 * 2 * 3 * 4,
+          ('b + 1) * 2 * 3 * 4,
+          'a + 1 + 'b + 2 + 'c + 3,
+          'a + 1 + 'b * 2 + 'c + 3,
+          Rand(0) * 1 * 2 * 3 * 4)
+
+    val optimized = Optimize.execute(originalQuery.analyze)
+
+    val correctAnswer =
+      testRelation
+        .select(
+          ('a + 10).as("((3 + ((1 + a) + 2)) + 4)"),
+          ('b * 24).as("((((b * 1) * 2) * 3) * 4)"),
+          (('b + 1) * 24).as("((((b + 1) * 2) * 3) * 4)"),
+          ('a + 'b + 'c + 6).as("(((((a + 1) + b) + 2) + c) + 3)"),
+          ('a + 'b * 2 + 'c + 4).as("((((a + 1) + (b * 2)) + c) + 3)"),
+          Rand(0) * 1 * 2 * 3 * 4)
+        .analyze
+
+    comparePlans(optimized, correctAnswer)
+  }
+}